Spatial range of autocrine signaling: modeling and computational analysis

Macroscopic quorum sensing sustains differentiating embryonic stem cells

Cells can secrete molecules that help each other's replication. In cell cultures, chemical signals might diffuse only within a cell colony or between colonies. A chemical signal's interaction length-how far apart interacting cells are-is often assumed to be some value without rigorous justifications because molecules' invisible paths and complex multicellular geometries pose challenges. Here we present an approach, combining mathematical models and experiments, for determining a chemical signal's interaction length. With murine embryonic stem (ES) cells as a testbed, we found that differentiating ES cells secrete FGF4, among others, to communicate over many millimeters in cell culture dishes and, thereby, form a spatially extended, macroscopic entity that grows only if its centimeter-scale population density is above a threshold value. With this 'macroscopic quorum sensing', an isolated macroscopic, but not isolated microscopic, colony can survive differentiation. Our integrated approach can determine chemical signals' interaction lengths in generic multicellular communities.

Engineered Tissue Models to Replicate Dynamic Interactions within the Hematopoietic Stem Cell Niche

Hematopoietic stem cells are the progenitors of the blood and immune system and represent the most widely used regenerative therapy. However, their rarity and limited donor base necessitate the design of ex vivo systems that support HSC expansion without the loss of long-term stem cell activity. This review describes recent advances in biomaterials systems to replicate features of the hematopoietic niche. Inspired by the native bone marrow, these instructive biomaterials provide stimuli and cues from cocultured niche-associated cells to support HSC encapsulation and expansion. Engineered systems increasingly enable study of the dynamic nature of the matrix and biomolecular environment as well as the role of cell-cell signaling (e.g., autocrine feedback vs paracrine signaling between dissimilar cells). The inherent coupling of material properties, biotransport of cell-secreted factors, and cell-mediated remodeling motivate dynamic biomaterial systems as well as characterization and modeling tools capable of evaluating a temporally evolving tissue microenvironment. Recent advances in HSC identification and tracking, model-based experimental design, and single-cell culture platforms facilitate the study of the effect of constellations of matrix, cell, and soluble factor signals on HSC fate. While inspired by the HSC niche, these tools are amenable to the broader stem cell engineering community.

Clustering of catalytic nanocompartments for enhancing an extracellular non-native cascade reaction

Compartmentalization is fundamental in nature, where the spatial segregation of biochemical reactions within and between cells ensures optimal conditions for the regulation of cascade reactions. While the distance between compartments or their interaction are essential parameters supporting the efficiency of bio-reactions, so far they have not been exploited to regulate cascade reactions between bioinspired catalytic nanocompartments. Here, we generate individual catalytic nanocompartments (CNCs) by encapsulating within polymersomes or attaching to their surface enzymes involved in a cascade reaction and then, tether the polymersomes together into clusters. By conjugating complementary DNA strands to the polymersomes' surface, DNA hybridization drove the clusterization process of enzyme-loaded polymersomes and controlled the distance between the respective catalytic nanocompartments. Owing to the close proximity of CNCs within clusters and the overall stability of the cluster architecture, the cascade reaction between spatially segregated enzymes was significantly more efficient than when the catalytic nanocompartments were not linked together by DNA duplexes. Additionally, residual DNA single strands that were not engaged in clustering, allowed for an interaction of the clusters with the cell surface as evidenced by A549 cells, where clusters decorating the surface endowed the cells with a non-native enzymatic cascade. The self-organization into clusters of catalytic nanocompartments confining different enzymes of a cascade reaction allows for a distance control of the reaction spaces which opens new avenues for highly efficient applications in domains such as catalysis or nanomedicine.

Encapsulation of murine hematopoietic stem and progenitor cells in a thiol-crosslinked maleimide-functionalized gelatin hydrogel

Biomaterial platforms are an integral part of stem cell biomanufacturing protocols. The collective biophysical, biochemical, and cellular cues of the stem cell niche microenvironment play an important role in regulating stem cell fate decisions. Three-dimensional (3D) culture of stem cells within biomaterials provides a route to present biophysical and biochemical stimuli through cell-matrix interactions and cell-cell interactions via secreted biomolecules. Herein, we describe a maleimide-functionalized gelatin (GelMAL) hydrogel that can be crosslinked via thiol-Michael addition click reaction for the encapsulation of sensitive stem cell populations. The maleimide functional units along the gelatin backbone enables gelation via the addition of a dithiol crosslinker without requiring external stimuli (e.g., UV light, photoinitiator), thereby reducing reactive oxide species generation. Additionally, the versatility of crosslinker selection enables easy insertion of thiol-containing bioactive or bioinert motifs. Hematopoietic stem cells (HSCs) and mesenchymal stem cells (MSCs) were encapsulated in GelMAL, with mechanical properties tuned to mimic the in vivo bone marrow niche. We report the insertion of a cleavable peptide crosslinker that can be degraded by the proteolytic action of Sortase A, a mammalian-inert enzyme. Notably, Sortase A exposure preserves stem cell surface markers, which are an essential metric of hematopoietic activity used in immunophenotyping. This novel GelMAL system enables a route to produce artificial stem cell niches with tunable biophysical properties, intrinsic cell-interaction motifs, and orthogonal addition of bioactive crosslinks. STATEMENT OF SIGNIFICANCE: We describe a maleimide-functionalized gelatin hydrogel that can be crosslinked via a thiol-maleimide mediated click reaction to form a stable hydrogel without the production of reactive oxygen species typical in light-based crosslinking. The mechanical properties can be tuned to match the in vivo bone marrow microenvironment for hematopoietic stem cell culture. Additionally, we report inclusion of a peptide crosslinker that can be cleaved via the proteolytic action of Sortase A and show that Sortase A exposure does not degrade sensitive surface marker expression patterns. Together, this approach reduces stem cell exposure to reactive oxygen species during hydrogel gelation and enables post-culture quantitative assessment of stem cell phenotype.

A local regulatory T cell feedback circuit maintains immune homeostasis by pruning self-activated T cells

A fraction of mature T cells can be activated by peripheral self-antigens, potentially eliciting host autoimmunity. We investigated homeostatic control of self-activated T cells within unperturbed tissue environments by combining high-resolution multiplexed and volumetric imaging with computational modeling. In lymph nodes, self-activated T cells produced interleukin (IL)-2, which enhanced local regulatory T cell (Treg) proliferation and inhibitory functionality. The resulting micro-domains reciprocally constrained inputs required for damaging effector responses, including CD28 co-stimulation and IL-2 signaling, constituting a negative feedback circuit. Due to these local constraints, self-activated T cells underwent transient clonal expansion, followed by rapid death ("pruning"). Computational simulations and experimental manipulations revealed the feedback machinery's quantitative limits: modest reductions in Treg micro-domain density or functionality produced non-linear breakdowns in control, enabling self-activated T cells to subvert pruning. This fine-tuned, paracrine feedback process not only enforces immune homeostasis but also establishes a sharp boundary between autoimmune and host-protective T cell responses.

Stromal Cell-Derived Factor-1a Autocrine/Paracrine Signaling Contributes to Spatiotemporal Gradients in the Brain

INTRODUCTION

Stromal cell derived factor-1a (SDF-1a) and its receptor CXCR4 modulate stem cell recruitment to neural injury sites. SDF-1a gradients originating from injury sites contribute to chemotactic cellular recruitment. To capitalize on this injury-induced cell recruitment, further investigation of SDF-1a/CXCR4 signaling dynamics are warranted. Here, we studied how exogenous SDF-1a delivery strategies impact spatiotemporal SDF-1a levels and the role autocrine/paracrine signaling plays.

METHODS

We first assessed total SDF-1a and CXCR4 levels over the course of 7 days following intracortical injection of either bolus SDF-1a or SDF-1a loaded nanoparticles in CXCR4-EGFP mice. We then investigated cellular contributors to SDF-1a autocrine/paracrine signaling via time course in vitro measurements of SDF-1a and CXCR4 gene expression following exogenous SDF-1a application. Lastly, we created mathematical models that could recapitulate our in vivo observations.

RESULTS

In vivo, we found sustained total SDF-1a levels beyond 3 days post injection, indicating endogenous SDF-1a production. We confirmed in vitro that microglia, astrocytes, and brain endothelial cells significantly change SDF-1a and CXCR4 expression after exposure. We found that diffusion-only based mathematical models were unable to capture in vivo SDF-1a spatial distribution. Adding autocrine/paracrine mechanisms to the model allowed for SDF-1a temporal trends to be modeled accurately, indicating it plays an essential role in SDF-1a sustainment.

CONCLUSIONS

We conclude that autocrine/paracrine dynamics play a role in endogenous SDF-1a levels in the brain following exogenous delivery. Implementation of these dynamics are necessary to improving SDF-1a delivery strategies. Further, mathematical models introduced here may be utilized in predicting future outcomes based upon new biomaterial designs.

Cytokine-mediated communication: a quantitative appraisal of immune complexity

Intercellular communication mediated by cytokines is the main mechanism by which cells of the immune system talk to each other. Many aspects of cytokine signalling in the immune system have been explored in great detail at the structural, biophysical, biochemical and cellular levels. However, a systematic understanding of the quantitative rules that govern cytokine-mediated cell-to-cell communication is still lacking. Here, we discuss recent efforts in the field of systems immunology to bring about a quantitative understanding of cytokine-mediated communication between leukocytes and to provide novel insights into the orchestration of immune responses and inflammation.

Modeling cell-cell communication for immune systems across space and time

Communicating is crucial for cells to coordinate their behaviors. Immunological processes, involving diverse cytokines and cell types, are ideal for developing frameworks for modeling coordinated behaviors of cells. Here, we review recent studies that combine modeling and experiments to reveal how immune systems use autocrine, paracrine, and juxtacrine signals to achieve behaviors such as controlling population densities and hair regenerations. We explain that models are useful because one can computationally vary numerous parameters, in experimentally infeasible ways, to evaluate alternate immunological responses. For each model, we focus on the length-scales and time-scales involved and explain why integrating multiple length-scales and time-scales in a model remain challenging. We suggest promising modeling strategies for meeting this challenge and their practical consequences.

Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies

Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.

A systems perspective of heterocellular signaling

Signal exchange between different cell types is essential for development and function of multicellular organisms, and its dysregulation is causal in many diseases. Unfortunately, most cell-signaling work has employed single cell types grown under conditions unrelated to their native context. Recent technical developments have started to provide the tools needed to follow signaling between multiple cell types, but gaps in the information they provide have limited their usefulness in building realistic models of heterocellular signaling. Currently, only targeted assays have the necessary sensitivity, selectivity, and spatial resolution to usefully probe heterocellular signaling processes, but these are best used to test specific, mechanistic models. Decades of systems biology research with monocultures has provided a solid foundation for building models of heterocellular signaling, but current models lack a realistic description of regulated proteolysis and the feedback processes triggered within and between cells. Identification and understanding of key regulatory processes in the extracellular environment and of recursive signaling patterns between cells will be essential to building predictive models of heterocellular systems.

Statistical Dynamics of Spatial-Order Formation by Communicating Cells

Communicating cells can coordinate their gene expressions to form spatial patterns, generating order from disorder. Ubiquitous "secrete-and-sense cells" secrete and sense the same molecule to do so. Here we present a modeling framework-based on cellular automata and mimicking approaches of statistical mechanics-for understanding how secrete-and-sense cells with bistable gene expression, from disordered beginnings, can become spatially ordered by communicating through rapidly diffusing molecules. Classifying lattices of cells by two "macrostate" variables-"spatial index," measuring degree of order, and average gene-expression level-reveals a conceptual picture: a group of cells behaves as a single particle, in an abstract space, that rolls down on an adhesive "pseudo-energy landscape" whose shape is determined by cell-cell communication and an intracellular gene-regulatory circuit. Particles rolling down the landscape represent cells becoming more spatially ordered. We show how to extend this framework to more complex forms of cellular communication.

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Resolving cancer-stroma interfacial signalling and interventions with micropatterned tumour-stromal assays

Tumor-stromal interactions are a determining factor in cancer progression. In vivo, the interaction interface is associated with spatially-resolved distributions of cancer and stromal phenotypes. Here, we establish a micropatterned tumor-stromal assay (μTSA) with laser capture microdissection to control the location of co-cultured cells and analyze bulk and interfacial tumor-stromal signaling in driving cancer progression. μTSA reveals a spatial distribution of phenotypes in concordance with human estrogen receptor-positive (ER+) breast cancer samples, and heterogeneous drug activity relative to the tumor-stroma interface. Specifically, an unknown mechanism of reversine is shown in targeting tumor-stromal interfacial interactions using ER+ MCF-7 breast cancer and bone marrow-derived stromal cells. Reversine suppresses MCF-7 tumor growth and bone metastasis in vivo by reducing tumor stromalization including collagen deposition and recruitment of activated stromal cells. This study advocates μTSA as a platform for studying tumor microenvironmental interactions and cancer field effects with applications in drug discovery and development.

Autocrine FGF feedback can establish distinct states of Nanog expression in pluripotent stem cells: a computational analysis

Background

The maintenance of stem cell pluripotency is controlled by a core cluster of transcription factors, NANOG, OCT4 and SOX2 – genes that jointly regulate each other’s expression. The expression of some of these genes, especially of Nanog, is heterogeneous in a population of undifferentiated stem cells in culture. Transient changes in expression levels, as well as heterogeneity of the population is not restricted to this core regulator, but involve a large number of other genes that include growth factors, transcription factors or signal transduction proteins.

Results

As the molecular mechanisms behind NANOG expression heterogeneity is not yet understood, we explore by computational modeling the core transcriptional regulatory circuit and its input from autocrine FGF signals that act through the MAP kinase cascade. We argue that instead of negative feedbacks within the core NANOG-OCT4-SOX2 transcriptional regulatory circuit, autocrine signaling loops such as the Esrrb - FGF - ERK feedback considered here are likely to generate distinct sub-states within the “ON” state of the core Nanog switch. Thus, the experimentally observed fluctuations in Nanog transcription levels are best explained as noise-induced transitions between negative feedback-generated sub-states. We also demonstrate that ERK phosphorilation is altered and being anti-correlated with fluctuating Nanog expression – in accord with model simulations. Our modeling approach assigns an empirically testable function to the transcriptional regulators Klf4 and Esrrb, and predict differential regulation of FGF family members.

Conclusions

We argue that slow fluctuations in Nanog expression likely reflect individual cell-specific changes in parameters of an autocrine feedback loop, such as changes in ligand capture efficiency, receptor numbers or the presence of crosstalks within the MAPK signal transduction pathway. We proposed a model that operates with binding affinities of multiple transcriptional regulators of pluripotency, and the activity of an autocrine signaling pathway. The resulting model produces varied expression levels of several components of pluripotency regulation, largely consistent with empirical observations reported previously and in this present work.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0112-4) contains supplementary material, which is available to authorized users.

Equilibrium and dynamic design principles for binding molecules engineered for reagentless biosensors

Reagentless biosensors rely on the interaction of a binding partner and its target to generate a change in fluorescent signal using an environment-sensitive fluorophore or Förster resonance energy transfer. Binding affinity can exert a significant influence on both the equilibrium and the dynamic response characteristics of such a biosensor. We here develop a kinetic model for the dynamic performance of a reagentless biosensor. Using a sinusoidal signal for ligand concentration, our findings suggest that it is optimal to use a binding moiety whose equilibrium dissociation constant matches that of the average predicted input signal, while maximizing both the association rate constant and the dissociation rate constant at the necessary ratio to create the desired equilibrium constant. Although practical limitations constrain the attainment of these objectives, the derivation of these design principles provides guidance for improved reagentless biosensor performance and metrics for quality standards in the development of biosensors. These concepts are broadly relevant to reagentless biosensor modalities.

A computational kinetic model of diffusion for molecular systems

Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10-100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS.

Secreting and sensing the same molecule allows cells to achieve versatile social behaviors

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core "secrete-and-sense" circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self-communication and neighbor communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself and social through quorum sensing, and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

Mechanotransduction

Physical forces are central players in development and morphogenesis, provide an ever-present backdrop influencing physiological functions, and contribute to a variety of pathologies. Mechanotransduction encompasses the rich variety of ways in which cells and tissues convert cues from their physical environment into biochemical signals. These cues include tensile, compressive and shear stresses, and the stiffness or elastic modulus of the tissues in which cells reside. This article focuses on the proximal events that lead directly from a change in physical state to a change in cell-signaling state. A large body of evidence demonstrates a prominent role for the extracellular matrix, the intracellular cytoskeleton, and the cell matrix adhesions that link these networks in transduction of the mechanical environment. Recent work emphasizes the important role of physical unfolding or conformational changes in proteins induced by mechanical loading, with examples identified both within the focal adhesion complex at the cell-matrix interface and in extracellular matrix proteins themselves. Beyond these adhesion and matrix-based mechanisms, classical and new mechanisms of mechanotransduction reside in stretch-activated ion channels, the coupling of physical forces to interstitial autocrine and paracrine signaling, force-induced activation of extracellular proteins, and physical effects directly transmitted to the cell's nucleus. Rapid progress is leading to detailed delineation of molecular mechanisms by which the physical environment shapes cellular signaling events, opening up avenues for exploring how mechanotransduction pathways are integrated into physiological and pathophysiological cellular and tissue processes.

Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor-ligand interactions in signalling response mechanisms

Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley-Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir-Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.

Cell surface concentrations and concentration ranges for testing in vitro autocrine loops and small molecules

A common assumption made when performing in vitro cellular assays is that the concentration of substances in the culture system is uniform. However, since the cells that internalize and secrete substances reside at the bottom of the well, it is conceivable that a concentration gradient could arise across the fluid layer. Importantly, the concentration of a substance in the vicinity of a cell, which is the concentration of interest, cannot be measured via existing methods. In this work a simple strategy for estimating the concentration of a chemical species at the surface of a cell is presented. Finally, this result is used to outline a method for determining the appropriate concentration ranges for testing in vitro autocrine loops and small molecules.

Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: incorporating EGFR signaling pathway and angiogenesis

Background

The epidermal growth factor receptor (EGFR) signaling pathway and angiogenesis in brain cancer act as an engine for tumor initiation, expansion and response to therapy. Since the existing literature does not have any models that investigate the impact of both angiogenesis and molecular signaling pathways on treatment, we propose a novel multi-scale, agent-based computational model that includes both angiogenesis and EGFR modules to study the response of brain cancer under tyrosine kinase inhibitors (TKIs) treatment.

Results

The novel angiogenesis module integrated into the agent-based tumor model is based on a set of reaction–diffusion equations that describe the spatio-temporal evolution of the distributions of micro-environmental factors such as glucose, oxygen, TGFα, VEGF and fibronectin. These molecular species regulate tumor growth during angiogenesis. Each tumor cell is equipped with an EGFR signaling pathway linked to a cell-cycle pathway to determine its phenotype. EGFR TKIs are delivered through the blood vessels of tumor microvasculature and the response to treatment is studied.

Conclusions

Our simulations demonstrated that entire tumor growth profile is a collective behaviour of cells regulated by the EGFR signaling pathway and the cell cycle. We also found that angiogenesis has a dual effect under TKI treatment: on one hand, through neo-vasculature TKIs are delivered to decrease tumor invasion; on the other hand, the neo-vasculature can transport glucose and oxygen to tumor cells to maintain their metabolism, which results in an increase of cell survival rate in the late simulation stages.

Balancing speed and accuracy of polyclonal T cell activation: a role for extracellular feedback

BACKGROUND

Extracellular feedback is an abundant module of intercellular communication networks, yet a detailed understanding of its role is still lacking. Here, we study interactions between polyclonal activated T cells that are mediated by IL-2 extracellular feedback as a model system.

RESULTS

Using mathematical modeling we show that extracellular feedback can give rise to opposite outcomes: competition or cooperation between interacting T cells, depending on their relative levels of activation. Furthermore, the outcome of the interaction also depends on the relative timing of activation of the cells. A critical time window exists after which a cell that has been more strongly activated nevertheless cannot exclude an inferior competitor.

CONCLUSIONS

In a number of experimental studies of polyclonal T-cell systems, outcomes ranging from cooperation to competition as well as time dependent competition were observed. Our model suggests that extracellular feedback can contribute to these observed behaviors as it translates quantitative differences in T cells' activation strength and in their relative activation time into qualitatively different outcomes. We propose extracellular feedback as a general mechanism that can balance speed and accuracy - choosing the most suitable responders out of a polyclonal population under the clock of an escalating threat.

Modular design of artificial tissue homeostasis: robust control through synthetic cellular heterogeneity

Synthetic biology efforts have largely focused on small engineered gene networks, yet understanding how to integrate multiple synthetic modules and interface them with endogenous pathways remains a challenge. Here we present the design, system integration, and analysis of several large scale synthetic gene circuits for artificial tissue homeostasis. Diabetes therapy represents a possible application for engineered homeostasis, where genetically programmed stem cells maintain a steady population of β-cells despite continuous turnover. We develop a new iterative process that incorporates modular design principles with hierarchical performance optimization targeted for environments with uncertainty and incomplete information. We employ theoretical analysis and computational simulations of multicellular reaction/diffusion models to design and understand system behavior, and find that certain features often associated with robustness (e.g., multicellular synchronization and noise attenuation) are actually detrimental for tissue homeostasis. We overcome these problems by engineering a new class of genetic modules for ‘synthetic cellular heterogeneity’ that function to generate beneficial population diversity. We design two such modules (an asynchronous genetic oscillator and a signaling throttle mechanism), demonstrate their capacity for enhancing robust control, and provide guidance for experimental implementation with various computational techniques. We found that designing modules for synthetic heterogeneity can be complex, and in general requires a framework for non-linear and multifactorial analysis. Consequently, we adapt a ‘phenotypic sensitivity analysis’ method to determine how functional module behaviors combine to achieve optimal system performance. We ultimately combine this analysis with Bayesian network inference to extract critical, causal relationships between a module's biochemical rate-constants, its high level functional behavior in isolation, and its impact on overall system performance once integrated.

Over the last decade several relatively small synthetic gene networks have been successfully implemented and characterized, including oscillators, toggle switches, and intercellular communication systems. However, the ability to engineer large-scale synthetic gene networks for controlling multicellular systems with predictable and robust behavior remains a challenge. Here we present a novel combination of computational methods to aid the iterative design and optimization of such synthetic biological systems. We apply these methods to the design and analysis of an artificial tissue homeostasis system that exhibits coordinated control of cellular proliferation, differentiation, and cell-death. Achieving artificial tissue homeostasis would be therapeutically relevant for diseases such as Type I diabetes, for instance by transplanting genetically engineered stem cells that stably maintain populations of insulin-producing beta-cells despite normal cell death and autoimmune attacks. To manage complexity in the design process, we employ principles of logic abstraction and modularity and investigate their limits in biological networks. In this work, we find factors often associated with robustness (e.g., multicellular synchronization and noise attenuation) to be actually detrimental, and overcome these problems by engineering genetic modules that generate beneficial population heterogeneity. A combination of computational methods elucidates how these modules function to enhance robust control, and provides guidance for experimental implementation.

Design principles of cell circuits with paradoxical components

Biological systems display complex networks of interactions both at the level of molecules inside the cell and at the level of interactions between cells. Networks of interacting molecules, such as transcription networks, have been shown to be composed of recurring circuits called network motifs, each with specific dynamical functions. Much less is known about the possibility of such circuit analysis in networks made of communicating cells. Here, we study models of circuits in which a few cell types interact by means of signaling molecules. We consider circuits of cells with architectures that seem to recur in immunology. An intriguing feature of these circuits is their use of signaling molecules with a pleiotropic or paradoxical role, such as cytokines that increase both cell growth and cell death. We find that pleiotropic signaling molecules can provide cell circuits with systems-level functions. These functions include for different circuits maintenance of homeostatic cell concentrations, robust regulation of differentiation processes, and robust pulses of cells or cytokines.

Effects of convective transport on chemical signal propagation in epithelia

We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of the convective transport. If the signal propagates downstream, the region of high velocities becomes much broader and spreads over several orders of magnitude of the binding constant. When the convective transport is oriented against the propagating signal, either velocity of the traveling front wave is slowed down or the traveling front wave can stop or reverse the direction of propagation. More importantly, chemical signal in epithelial systems influenced by the convective transport can propagate almost independently of the ligand-receptor binding constant in a broad range of this parameter. Furthermore, we found that the effects of the convective transport becomes more significant in systems where either the characteristic dimension of the extracellular space is larger/comparable with the spatial extent of the ligand diffusion trafficking or the ligand-receptor binding/ligand diffusion rate ratio is high.

Model of the initiation of signal transduction by ligands in a cell culture: simulation of molecules near a plane membrane comprising receptors

Cell communication is a key mechanism in tissue responses to radiation. Several molecules are implicated in radiation-induced signaling between cells, but their contributions to radiation risk are poorly understood. Meanwhile, Green's functions for diffusion-influenced reactions have appeared in the literature, which are applied to describe the diffusion of molecules near a plane membrane comprising bound receptors with the possibility of reversible binding of a ligand and activation of signal transduction proteins by the ligand-receptor complex. We have developed Brownian dynamics algorithms to simulate particle histories in this system which can accurately reproduce the theoretical distribution of distances of a ligand from the membrane, the number of reversibly bound particles, and the number of receptor complexes activating signaling proteins as a function of time, regardless of the number of time steps used for the simulation. These simulations will be of great importance to model interactions at low doses where stochastic effects induced by a small number of molecules or interactions come into play.

Subcellular resolution mapping of endogenous cytokine secretion by nano-plasmonic-resonator sensor array

Local extracellular signaling is central for cellular interactions and organizations. We report a novel sensing technique to interrogate extracellular signaling at the subcellular level. We developed an in situ immunoassay based on giant optical enhancement of a tunable nano-plasmonic-resonator array fabricated by nanoimprint lithography. Our nanoplasmonic device significantly increases the signal-to-noise ratio to enable the first time submicrometer resolution quantitative mapping of endogenous cytokine secretion. Our study shows a markedly high local interleukin-2 (IL-2) concentration within the immediate vicinity of the cell which finally validates a decades-old hypothesis on autocrine physiological concentration and spatial range. This general sensing technique can be applied for a broad range of cellular communication studies to improve our understanding of subcellular signaling and function.

Microfluidic perfusion for regulating diffusible signaling in stem cells

BACKGROUND

Autocrine & paracrine signaling are widespread both in vivo and in vitro, and are particularly important in embryonic stem cell (ESC) pluripotency and lineage commitment. Although autocrine signaling via fibroblast growth factor-4 (FGF4) is known to be required in mouse ESC (mESC) neuroectodermal specification, the question of whether FGF4 autocrine signaling is sufficient, or whether other soluble ligands are also involved in fate specification, is unknown. The spatially confined and closed-loop nature of diffusible signaling makes its experimental control challenging; current experimental approaches typically require prior knowledge of the factor/receptor in order to modulate the loop. A new approach explored in this work is to leverage transport phenomena at cellular resolution to downregulate overall diffusible signaling through the physical removal of cell-secreted ligands.

METHODOLOGY/PRINCIPAL FINDINGS

We develop a multiplex microfluidic platform to continuously remove cell-secreted (autocrine\paracrine) factors to downregulate diffusible signaling. By comparing cell growth and differentiation in side-by-side chambers with or without added cell-secreted factors, we isolate the effects of diffusible signaling from artifacts such as shear, nutrient depletion, and microsystem effects, and find that cell-secreted growth factor(s) are required during neuroectodermal specification. Then we induce FGF4 signaling in minimal chemically defined medium (N2B27) and inhibit FGF signaling in fully supplemented differentiation medium with cell-secreted factors to determine that the non-FGF cell-secreted factors are required to promote growth of differentiating mESCs.

CONCLUSIONS/SIGNIFICANCE

Our results demonstrate for the first time that flow can downregulate autocrine\paracrine signaling and examine sufficiency of extracellular factors. We show that autocrine\paracrine signaling drives neuroectodermal commitment of mESCs through both FGF4-dependent and -independent pathways. Overall, by uncovering autocrine\paracrine processes previously hidden in conventional culture systems, our results establish microfluidic perfusion as a technique to study and manipulate diffusible signaling in cell systems.

Pattern, growth, and control

Systems biology seeks not only to discover the machinery of life but to understand how such machinery is used for control, i.e., for regulation that achieves or maintains a desired, useful end. This sort of goal-directed, engineering-centered approach also has deep historical roots in developmental biology. Not surprisingly, developmental biology is currently enjoying an influx of ideas and methods from systems biology. This Review highlights current efforts to elucidate design principles underlying the engineering objectives of robustness, precision, and scaling as they relate to the developmental control of growth and pattern formation. Examples from vertebrate and invertebrate development are used to illustrate general lessons, including the value of integral feedback in achieving set-point control; the usefulness of self-organizing behavior; the importance of recognizing and appropriately handling noise; and the absence of "free lunch." By illuminating such principles, systems biology is helping to create a functional framework within which to make sense of the mechanistic complexity of organismal development.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Effects of ionizing radiation on cell-to-cell communication

Cell-to-cell signaling has become a significant issue in radiation biology due to experimental evidence, accumulated primarily since the early 1990s, of radiation-induced bystander effects. Several candidate mediators involved in cell-to-cell communication have been investigated and proposed as being responsible for this phenomenon, but the current investigation techniques (both theoretical and experimental) of the mechanisms involved, due to the particular set-up of each experiment, result in experimental data that often are not directly comparable. In this study, a comprehensive approach was adopted to describe cell-to-cell communication (focusing on cytokine signaling) and its modulation by external agents such as ionizing radiation. The aim was also to provide integrated theoretical instruments and experimental data to help in understanding the peculiarities of in vitro experiments. Theoretical/modeling activities were integrated with experimental measurements by (1) redesigning a cybernetic model (proposed in its original form in the 1950s) to frame cell-to-cell communication processes, (2) implementing and developing a mathematical model, and (3) designing and carrying out experiments to quantify key parameters involved in intercellular signaling (focusing as a pilot study on the release and decay of IL-6 molecules and their modulation by radiation). This formalization provides an interpretative framework for understanding the intercellular signaling and in particular for focusing on the study of cell-to-cell communication in a "step-by-step" approach. Under this model, the complex phenomenon of signal transmission was reduced where possible into independent processes to investigate them separately, providing an evaluation of the role of cell communication to guarantee and maintain the robustness of the in vitro experimental systems against the effects of perturbations.

Quantitative understanding of cell signaling: the importance of membrane organization

Systems biology modeling of signal transduction pathways traditionally employs ordinary differential equations, deterministic models based on the assumptions of spatial homogeneity. However, this can be a poor approximation for certain aspects of signal transduction, especially its initial steps: the cell membrane exhibits significant spatial organization, with diffusion rates approximately two orders of magnitude slower than those in the cytosol. Thus, to unravel the complexities of signaling pathways, quantitative models must consider spatial organization as an important feature of cell signaling. Furthermore, spatial separation limits the number of molecules that can physically interact, requiring stochastic simulation methods that account for individual molecules. Herein, we discuss the need for mathematical models and experiments that appreciate the importance of spatial organization in the membrane.

Quantifying the proteolytic release of extracellular matrix-sequestered VEGF with a computational model

Background

VEGF proteolysis by plasmin or matrix metalloproteinases (MMPs) is believed to play an important role in regulating vascular patterning in vivo by releasing VEGF from the extracellular matrix (ECM). However, a quantitative understanding of the kinetics of VEGF cleavage and the efficiency of cell-mediated VEGF release is currently lacking. To address these uncertainties, we develop a molecular-detailed quantitative model of VEGF proteolysis, used here in the context of an endothelial sprout.

Methodology and Findings

To study a cell's ability to cleave VEGF, the model captures MMP secretion, VEGF-ECM binding, VEGF proteolysis from VEGF₁₆₅ to VEGF₁₁₄ (the expected MMP cleavage product of VEGF₁₆₅) and VEGF receptor-mediated recapture. Using experimental data, we estimated the effective bimolecular rate constant of VEGF₁₆₅ cleavage by plasmin to be 328 M⁻¹s⁻¹ at 25°C, which is relatively slow compared to typical MMP-ECM proteolysis reactions. While previous studies have implicated cellular proteolysis in growth factor processing, we show that single cells do not individually have the capacity to cleave VEGF to any appreciable extent (less than 0.1% conversion). In addition, we find that a tip cell's receptor system will not efficiently recapture the cleaved VEGF due to an inability of cleaved VEGF to associate with Neuropilin-1.

Conclusions

Overall, VEGF₁₆₅ cleavage in vivo is likely to be mediated by the combined effect of numerous cells, instead of behaving in a single-cell-directed, autocrine manner. We show that heparan sulfate proteoglycans (HSPGs) potentiate VEGF cleavage by increasing the VEGF clearance time in tissues. In addition, we find that the VEGF-HSPG complex is more sensitive to proteases than is soluble VEGF, which may imply its potential relevance in receptor signaling. Finally, according to our calculations, experimentally measured soluble protease levels are approximately two orders of magnitude lower than that needed to reconcile levels of VEGF cleavage seen in pathological situations.

Computational model and microfluidic platform for the investigation of paracrine and autocrine signaling in mouse embryonic stem cells

Autocrine and paracrine signaling mechanisms are traditionally difficult to study due to the recursive nature of the process and the sub-micromolar concentrations involved. This has proven to be especially limiting in the study of embryonic stem cells that might rely on such signaling for viability, self-renewal, and proliferation. To better characterize possible effects of autocrine and paracrine signaling in the setting of expanding stem cells, we developed a computational model assuming a critical need for cell-secreted survival factors. This model suggested that the precise way in which the removal of putative survival factors could affect stem cell survival in culture. We experimentally tested the predictions in mouse embryonic stem cells by taking advantage of a novel microfluidic device allowing removal of the cell-conditioned medium at defined time intervals. Experimental results in both serum-containing and defined N2B27 media confirmed computational model predictions, suggested existence of unknown survival factors with distinct rates of diffusion, and revealed an adaptive/selective phase in mouse embryonic stem cell response to a lack of paracrine signaling. We suggest that the described computational/experimental platform can be used to identify and study specific factors and pathways involved in a wide variety of paracrine signaling systems.

Autocrine signal transmission with extracellular ligand degradation

Traveling waves of cell signaling in epithelial layers orchestrate a number of important processes in developing and adult tissues. These waves can be mediated by positive feedback autocrine loops, a mode of cell signaling where binding of a diffusible extracellular ligand to a cell surface receptor can lead to further ligand release. We formulate and analyze a biophysical model that accounts for ligand-induced ligand release, extracellular ligand diffusion and ligand-receptor interaction. We focus on the case when the main mode for ligand degradation is extracellular and analyze the problem with the sharp threshold positive feedback nonlinearity. We derive expressions that link the speed of propagation and other characteristics of traveling waves to the parameters of the biophysical processes, such as diffusion rates, receptor expression level, etc. Analyzing the derived expressions we found that traveling waves in such systems can exhibit a number of unusual properties, e.g. non-monotonic dependence of the speed of propagation on ligand diffusivity. Our results for the fully developed traveling fronts can be used to analyze wave initiation from localized perturbations, a scenario that frequently arises in the in vitro models of epithelial wound healing, and guide future modeling studies of cell communication in epithelial layers.

Allovalency revisited: an analysis of multisite phosphorylation and substrate rebinding

The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations may be to increase the probability that, upon dissociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems is not well understood. Here, a self-consistent integral equation formalism for ligand rebinding, in conjunction with Monte Carlo simulations, is employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects are predicted. Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly. The model also predicts that ligand rebinding in itself appears insufficient to generate a highly cooperative biological response.

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.

Simulating non-small cell lung cancer with a multiscale agent-based model

BACKGROUND

The epidermal growth factor receptor (EGFR) is frequently overexpressed in many cancers, including non-small cell lung cancer (NSCLC). In silico modeling is considered to be an increasingly promising tool to add useful insights into the dynamics of the EGFR signal transduction pathway. However, most of the previous modeling work focused on the molecular or the cellular level only, neglecting the crucial feedback between these scales as well as the interaction with the heterogeneous biochemical microenvironment.

RESULTS

We developed a multiscale model for investigating expansion dynamics of NSCLC within a two-dimensional in silico microenvironment. At the molecular level, a specific EGFR-ERK intracellular signal transduction pathway was implemented. Dynamical alterations of these molecules were used to trigger phenotypic changes at the cellular level. Examining the relationship between extrinsic ligand concentrations, intrinsic molecular profiles and microscopic patterns, the results confirmed that increasing the amount of available growth factor leads to a spatially more aggressive cancer system. Moreover, for the cell closest to nutrient abundance, a phase-transition emerges where a minimal increase in extrinsic ligand abolishes the proliferative phenotype altogether.

CONCLUSION

Our in silico results indicate that in NSCLC, in the presence of a strong extrinsic chemotactic stimulus (and depending on the cell's location) downstream EGFR-ERK signaling may be processed more efficiently, thereby yielding a migration-dominant cell phenotype and overall, an accelerated spatio-temporal expansion rate.

Time and length scales of autocrine signals in three dimensions

A model of autocrine signaling in cultures of suspended cells is developed on the basis of the effective medium approximation. The fraction of autocrine ligands, the mean and distribution of distances traveled by paracrine ligands before binding, as well as the mean and distribution of the ligand lifetime are derived. Interferon signaling by dendritic immune cells is considered as an illustration.

Collective migration of an epithelial monolayer in response to a model wound

Using an original microfabrication-based technique, we experimentally study situations in which a virgin surface is presented to a confluent epithelium with no damage made to the cells. Although inspired by wound-healing experiments, the situation is markedly different from classical scratch wounding because it focuses on the influence of the free surface and uncouples it from the other possible contributions such as cell damage and/or permeabilization. Dealing with Madin-Darby canine kidney cells on various surfaces, we found that a sudden release of the available surface is sufficient to trigger collective motility. This migration is independent of the proliferation of the cells that mainly takes place on the fraction of the surface initially covered. We find that this motility is characterized by a duality between collective and individual behaviors. On the one hand, the velocity fields within the monolayer are very long range and involve many cells in a coordinated way. On the other hand, we have identified very active "leader cells" that precede a small cohort and destabilize the border by a fingering instability. The sides of the fingers reveal a pluricellular actin "belt" that may be at the origin of a mechanical signaling between the leader and the followers. Experiments performed with autocrine cells constitutively expressing hepatocyte growth factor (HGF) or in the presence of exogenous HGF show a higher average velocity of the border and no leader.

Autocrine production of insulin-like growth factor-I (IGF-I) affects paracellular transport across epithelial cells in vitro

Autocrine production of growth factors can have significant effects on cell activity. We report for the first time that autocrine production of insulin-like growth factor-I (IGF-I) alters paracellular transport across bovine mammary epithelial cells in vitro. Paracellular transport was assessed by measuring phenol red transport across mammary alveolar cells-large T antigen (MAC-T cells) derived from parental mammary epithelial cells, cultured on porous membranes and compared with two different transfected MAC-T cell lines that constitutively secrete IGF-I. Phenol red transport was essentially blocked in parental cell culture after six days, while IGF-I secreting cells provided essentially no barrier. Surprisingly, neither co-culture studies between parental and IGF-I-secreting cells nor addition of exogenous IGF-I or IGF-binding protein-3 reversed the phenol red transport properties. IGF-I-secreting cells did however express lower levels of the junction components occludin and E-cadherin than parental cells, suggesting that localized autocrine IGF-I activity might lead to increased permeability via changes in both the tight and adherens junction protein levels.

EGF-receptor-mediated mammary epithelial cell migration is driven by sustained ERK signaling from autocrine stimulation

EGF family ligands are synthesized as membrane-anchored precursors whose proteolytic release yields mature diffusible factors that can activate cell surface receptors in autocrine or paracrine mode. Expression of these ligands is altered in pathological states and in physiological processes, such as development and tissue regeneration. Despite the widely documented biological importance of autocrine EGF signaling, quantitative relationships between protease-mediated ligand release and consequent cell behavior have not been rigorously investigated. We thus explored the relationship between autocrine EGF release rates and cell behavioral responses along with activation of ERK, a key downstream signal, by expressing chimeric ligand precursors and modulating their proteolytic shedding using a metalloprotease inhibitor in human mammary epithelial cells. We found that ERK activation increased monotonically with increasing ligand release rate despite concomitant downregulation of EGF receptor levels. Cell migration speed was directly related to ligand release rate and proportional to steady-state phospho-ERK levels. Moreover, migration speed was significantly greater for autocrine stimulation compared with exogenous stimulation, even at comparable phospho-ERK levels. By contrast, cell proliferation rates were approximately equivalent at all ligand release rates and were similar regardless of whether the ligand was presented endogenously or exogenously. Thus, in our mammary epithelial cell system, migration and proliferation are differentially sensitive to the mode of EGF ligand presentation.

Optimal experimental design in an epidermal growth factor receptor signalling and down-regulation model

We apply the methods of optimal experimental design to a differential equation model for epidermal growth factor receptor signalling, trafficking and down-regulation. The model incorporates the role of a recently discovered protein complex made up of the E3 ubiquitin ligase, Cbl, the guanine exchange factor (GEF), Cool-1 (beta -Pix) and the Rho family G protein Cdc42. The complex has been suggested to be important in disrupting receptor down-regulation. We demonstrate that the model interactions can accurately reproduce the experimental observations, that they can be used to make predictions with accompanying uncertainties, and that we can apply ideas of optimal experimental design to suggest new experiments that reduce the uncertainty on unmeasurable components of the system.

Array feature size influences nucleic acid surface capture in DNA microarrays

Analyte affinity capture by surface-immobilized diagnostic agents is a routinely used assay format for profiling numerous medically and technologically important target analytes. These assays suffer from numerous performance limitations, including sensitivity and rapidity. Assay miniaturization is advocated to improve surface-capture performance, specifically exploiting the inverse relationship between analyte flux and capture feature size under mass transfer-limiting capture conditions that characterize many such assay formats. Reduced capture feature sizes, e.g., microarrays, are proposed to overcome mass transfer limitations, yet this is difficult to achieve across several size scales. This study validates certain advantages advocated for capture spot miniaturization using a rationale to understand surface capture miniaturization strategies. Experimentally derived immobilized ligand and target capture densities as a function of microspot size for DNA oligomers immobilized on model gold substrates are compared directly with theoretical analysis, validating the hypothesis that miniaturization yields many practical assay advantages. Specifically, results show that transitions from assay mass transfer limiting to kinetically limiting conditions as feature size decreases identify an optimal microspot size range for a specific bioassay system. Analytical advantages realized from such assay miniaturization are more uniform target-spot coverage and substantially increased rate of capture (hybridization), increasing assay signal and rapidity.

Interstitial flow and its effects in soft tissues

Interstitial flow plays important roles in the morphogenesis, function, and pathogenesis of tissues. To investigate these roles and exploit them for tissue engineering or to overcome barriers to drug delivery, a comprehensive consideration of the interstitial space and how it controls and affects such processes is critical. Here we attempt to review the many physical and mathematical correlations that describe fluid and mass transport in the tissue interstitium; the factors that control and affect them; and the importance of interstitial transport on cell biology, tissue morphogenesis, and tissue engineering. Finally, we end with some discussion of interstitial transport issues in drug delivery, cell mechanobiology, and cell homing toward draining lymphatics.